From the supplementary material of their 2022 study "Poor writing, not specialized concepts,
drives processing difficulty in legal language"¹ (in this example, embedded clauses, the best example of which, in my opinion, can be found in the final sentence of the paragraph hereinunder, are indicated by italics):

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It is understood by Lessees, standing liable for violating obligations inter se, hereinbefore set forth in Clause 3 of this real estate agreement, that Lessors shall be exempt from liability for any damages, to the maximum extent not prohibited by law, unless Lessors knew of the possibility of such damage and acted with scienter. Lessee's aggregate liability inter se for all claims, including those based on tort or statutory liability, is limited to $1000 by this agreement. Personal injury damages, limitations of liability of which, excepting those for emotional distress, this jurisdiction prohibits, are not affected by the foregoing provisions.

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"So much for plain language: An analysis of the accessibility of United
States federal laws over time"² clarifies what these researchers count as center-embedding:

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Center-embedded clauses.

Plain-language guidelines discourage the use of "convoluted" sentences, particularly those that are "loaded with dependent clauses" and which separate the "essential parts" of a sentence from each other (i.e. the subject, verb and object). The most notorious examples of such sentences contain center-embedded structures, in which a sentence or clause is embedded within the center of another sentence or clause ("all such payments and benefits, including the payments and benefits under Section 3(a) hereof, being hereinafter referred to as the 'Total Payments'"). Center-embedded structures cause processing difficulty for readers (Gibson, 1998) and have been shown to inhibit recall of legal content relative to clauses that have been un-embedded into separate sentences (Martinez, Mollica, & Gibson, 2021). Here we calculated the percentage of sentences in each corpus containing a center-embedded clause. We coded a sentence as containing a center-embedded clause if a predicate dependent clause as parsed by Stanza (i.e. clausal subjects, clausal complements, open clausal complements, adjectival clauses, and adverbial clauses) was followed by a word as opposed to an end-of-sentence punctuation mark.

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Most examples I've found seem to focus more strictly on constructions along the lines of:

The ice cream{that the boy [that the girl liked] bought} melted.³

As opposed to this one, which is not center-embedded:

The girl{that likes the boy [that bought the ice cream] } sang.

I'm not sure exactly how strict the definition of a center-embedded clause is meant to be. If it does mean only a phrase embedded within another phrase of the same type as described in the Wikipedia article, then aren't Martinez, et al. taking some liberties with it? Or is it really a broader concept than that?

Going back to the second paragraph of this comment, "including those based on tort or statutory liability" seems especially out of place. Does a mere parenthetical phrase -- and not a particularly disorienting one at that -- really count? It isn't a recursive relative clause of the kind I see people use to illustrate center-embedding.

The supporting information for "Even Laypeople Use Legalese"⁴ has what I assume are more examples of center-embedding according to these researchers (in the statutes linked):

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Any person who trafficks in marihuana by knowingly or intentionally manufacturing, distributing, dispensing, or cultivating or possessing with intent to manufacture, distribute, dispense, or cultivate, or by bringing into the commonwealth a net weight of fifty pounds or more of marihuana or a net weight of fifty pounds or more of any mixture containing marihuana shall, if the net weight of marihuana or any mixture thereof is [ . . . ] [f]ifty pounds or more, but less than one hundred pounds, be punished by a term of imprisonment in the state prison for not less than two and one-half nor more than fifteen years or by imprisonment in a jail or house of correction for not less than one nor more than two and one-half years.

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1. https://ars.els-cdn.com/content/image/1-s2.0-S00100277220005...

2. https://osf.io/preprints/psyarxiv/hpxqu

3. https://www.polyu.edu.hk/cbs/sjpolit/classes/cbs516/psycholi...

4. https://www.pnas.org/doi/suppl/10.1073/pnas.2405564121/suppl...